Homework 3

Matthew Jacobs

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I'm not really able to read C, but did the best I could. Flowcharts are rather sloppy. image-2.png image.png

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We see that using a larger timestep (1 year vs .001 year) causes the orbits to be very different. Rebound is even nice and warns us that our timestep is likely causing errors. When trying to compare the energy of the system, we don't see any difference between the two timestepping. I may have not utilized this function correctly.

We note that the WH and IAS15 give comparable results for the small timestep, while the larger timesteps are both quite different. From the literature we expect the IAS15 to be more accurate.

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We see the position of the comet (bottom particle in this plot) isn't very different in the full solar system. This is because the main actors on its orbit are the Sun and Jupiter (arguably Saturn too). The addition of the terrestrial planets and farther out ice giants don't seem to impact things terribly. I would argue the timestep produce the largest source of error, when going too large.

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So for Planet X with this orbit would need to be about 8 solar masses to cause a 10% shift in Pluto's Orbit. At this mass, it would be fusing and be quite luminous. Planet X, if it exists, likely has not been detected because it's mass is probably small enough that it's very difficulty to detect any diffence in the orbit of Pluto due to its gravity.